In the tracking of missiles and rockets for purposes such as guidance or intercept, it is common to use computer models of the vehicle to be guided or intercepted. These models receive sensor inputs from a variety of sensors, which give information relating to the current position and possibly other parameters. These measurements are subject to noise and bias. In this context, noise relates to stochastic random measurement processes at each measurement time, whereas bias relates to a stochastic random measurement process which is constant or common over the measurement period or succession of measurements. The noise and bias tend to obscure the sensed parameters, and the bias can introduce errors in the vehicle state estimates in those cases in which different sensors, each having its own bias, are used at different times during the vehicle's travel.
Prior art models which estimate the parameters of missiles or rockets in the boost phase assume non-linear models that incorporate certain dynamic or dynamical properties of the vehicle being tracked during state estimation or assume high order linear models to account for the nonlinear rocket motor acceleration. Specific acceleration and specific impulse are examples of dynamical properties used in non-linear models. Jerk (derivative of acceleration) and snap (derivative of jerk) are examples of the higher order states used in linear models. If the model is not consistent with the vehicle being tracked, the state estimates will be biased because of the assumptions made in the dynamic model. Put another way, the non-linear model that is used to determine the vehicle parameters assumes parameters of the vehicle, while the high order linear models may fail to sufficiently capture the nonlinear behavior of the vehicle accelerations, and the non-linear model may therefore be inherently biased by those assumptions. Thus, the current state-of-the-art in boost phase tracking models provides sub-optimal, degraded performance due to the fusing of multiple sensor measurements contaminated with sensor registration biases and also due to inadequacy of the dynamical modeling.
Improved models are desired for estimating parameters of a rocket or missile (a vehicle) in the boost phase with reduced bias.